Cremona's table of elliptic curves

3003 = 3 · 7 · 11 · 13

Field	Data	Notes
Atkin-Lehner	3+ 7- 11+ 13+	Signs for the Atkin-Lehner involutions
Class	3003d	Isogeny class
Conductor	3003	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	5760	Modular degree for the optimal curve
Δ	-3426316276383 = -1 · 310 · 74 · 11 · 133	Discriminant
Eigenvalues	1 3+  0 7- 11+ 13+  0 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-3465,117288]	[a1,a2,a3,a4,a6]
j	-4602875775513625/3426316276383	j-invariant
L	1.4576126225897	L(r)(E,1)/r!
Ω	0.72880631129485	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	48048cf1 9009k1 75075bf1 21021i1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3003d1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
1	+	0	-	+	+	0	-8	8	4	2	10	10	-6	-12	-2	12	-2	10	-4	10	-14	-4	-12	2

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Quadratic twists for elliptic curve 3003d1

-4	-3	5	-7	-11	13
48048cf1	9009k1	75075bf1	21021i1	33033g1	39039i1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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